How to Bend/curve edges
Sounds like you're looking for the Bevel Tool. Select the edges you want to bevel in Edit Mode, press Ctrl+B, drag the mouse to start beveling the edges, use the scroll wheel to set the number of segments.
For a more detailed description of the Bevel Tool read this article in the Blender Manual:
Bevel Edges
There's also a non-destructive way to bevel the edges:
Bevel Modifier